Question

What is the relation between rate constant and Activation energy?

Answer 1

1. Rate constant is the proportionality constant used in the rate law expression.
2. Rate law is the expression in which the reaction rate is given in the terms of molar concentrations of the reactants with each term raised to some power.
3. $$\begin{gathered} \mathrm{aA}+\mathrm{bB}\to \mathrm{cC} \\ \mathrm{Rate}=\frac{1}{\mathrm{c}}\frac{\mathrm{d}\left[\mathrm{C}\right]}{\mathrm{dt}}=-\frac{1}{\mathrm{a}}\frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=-\frac{1}{\mathrm{b}}\frac{\mathrm{d}\left[\mathrm{B}\right]}{\mathrm{dt}} \end{gathered}$$
4. Activation energy is the minimum energy required for a chemical reaction to occur.
5. The relation between the rate constant and the activation energy was given by Arrhenius.
   $$\begin{gathered} \mathrm{k}={\mathrm{Ae}}^{\frac{-\mathrm{Ea}}{\mathrm{RT}}} \\ \mathrm{where}\mathrm{k}\mathrm{is}\mathrm{the}\mathrm{rate}\mathrm{constant} \\ \mathrm{A}\mathrm{is}\mathrm{the}\mathrm{pre}\mathrm{exponential}\mathrm{factor} \\ \mathrm{Ea}\mathrm{is}\mathrm{the}\mathrm{Activation}\mathrm{energy} \\ \mathrm{R}\mathrm{is}\mathrm{the}\mathrm{gas}\mathrm{constant} \\ \mathrm{T}\mathrm{is}\mathrm{the}\mathrm{temperature} \end{gathered}$$